3
$\begingroup$

The following code displays three solutions to the logistic ODE with an animated points that follow the solutions.. My goal is to project the solutions on to a vertical phase line. I need to be able to create a phase line of exactly length as the x-axis and have the projected solutions move appropriately. As you can see my projections do not lie on a fixed length copy of the x-axis. Additionally, I want to plot fixed points at x=0 and x=1 and be able to set any color I want to the fixed and moving points. The phase line needs to be closer to the tx-plot as well.

Finally, I'd like to be able vary the parameter r and the initial value x0 in the solution formula (see Initialization code)

Please help relieve my frustration.

Manipulate[ y1[t_] = y[t, 0.2, 2]; y2[t_] = y[t, 0.2, 0.1]; y3[t_] = y[t, 0.2, -0.01]; If[s == 20, s = 0]; GraphicsRow[{ Plot[{y1[t], y2[t], y3[t], 0, 1}, {t, 0, 20}, ImageSize -> {600, 400}, PlotRange -> {{0, 20}, {-1, 2}}, PlotStyle -> {{Thick, Black}, {Thick, Black}, {Thick, Black}, {Thick, Black, Dashed}, {Thick, Black, Dashed}}, BaseStyle -> {FontSize -> 16}, Frame -> True, Axes -> False, FrameLabel -> {t, x}, RotateLabel -> False, AspectRatio -> 0.75, PlotRangePadding -> 0.1, Epilog -> {PointSize[0.02], Red, Point[{{s, y1[s]}, {s, y2[s]}, {s, y3[s]} }]}], Graphics[{PointSize[0.02], Red, Point[{{0, y1[s]}, {0, y2[s]}, {0, y3[s]} }]}]} ], {{s, 0, "FLOW"}, 0, 20, .01, ControlType -> Trigger, AnimationRate -> 3, AppearanceElements -> {"StepLeftButton", "StepRightButton", "PlayPauseButton", "ResetButton", "FasterSlowerButtons"}}, FrameLabel -> Style["One dimensional flow associated with logistic equation", 16, FontFamily -> "Helv"], Initialization -> (y[t_, r_, x0_] := 1/(1 + (1/x0 - 1) Exp[-r t])) ]

Mathematica graphics

Improve this question
$\endgroup$
7
  • 1
    $\begingroup$ Please format your question - the markdown help is just around the corner: mathematica.stackexchange.com/help/formatting $\endgroup$ Commented Mar 18, 2014 at 17:42
  • $\begingroup$ Should I use Dingus to convert to HTML? $\endgroup$ Commented Mar 18, 2014 at 17:54
  • $\begingroup$ @Stephen I already did it for you. Please read Yves' link $\endgroup$ Commented Mar 18, 2014 at 17:58
  • $\begingroup$ @Yves - What is the easiest way to convert my Mathematica code to Markdown formatting? $\endgroup$ Commented Mar 18, 2014 at 18:05
  • $\begingroup$ @Stephen The second and third sections of Yves' link explain code blocks and inline code. Are they not helpful? $\endgroup$ Commented Mar 18, 2014 at 18:06

1 Answer 1

Reset to default
4
$\begingroup$ 
Manipulate[ y1[t_, r_] := y[t, r, 2]; y2[t_, r_] := y[t, r, 0.1]; y3[t_, r_] := y[t, r, -0.01]; If[s == 20, s = 0]; Plot[{y1[t, r], y2[t, r], y3[t, r], 0, 1}, {t, 0, 20}, Frame -> True, Axes -> False, PlotRangePadding -> {{.1, 2}, {.1, .1}}, Epilog -> { PointSize[0.02], Red, Point[{{s, y1[s, r]}, {s, y2[s, r]}, {s, y3[s, r]}}], Black, Line[{{21, -2}, {21, 3}}], Blue, Point[{{21, y1[s, r]}, {21, y2[s, r]}, {21, y3[s, r]}}]}], {{s, 0, "FLOW"}, 0, 20, .01}, {{r, 0, "r"}, 0, 1, .01}, Initialization -> (y[t_, r_, x0_] := 1/(1 + (1/x0 - 1) Exp[-r t]))]

Mathematica graphics

Improve this answer
$\endgroup$
6
  • $\begingroup$ @bellsarius :-) $\endgroup$ Commented Mar 18, 2014 at 18:30
  • $\begingroup$ @bellsarius: I want to place a fixed circle at {21,0} and a point at {21,1} of color Green. I cannot do this within Epilog. $\endgroup$ Commented Mar 18, 2014 at 19:02
  • $\begingroup$ @bellsarius I want to plot fixed points at {21,0} and {21,1} and be able to set different colors to all of the points - both fixed & moving. $\endgroup$ Commented Mar 18, 2014 at 19:10
  • $\begingroup$ @Stephen Use the Epilog to plot the points and a ColorSetter control to choose the colors $\endgroup$ Commented Mar 18, 2014 at 19:23
  • 2
    $\begingroup$ @Stephen A few things: 1) I haven't proposed any "file" 2) You never mentioned exporting to a CDF in the question 3) Change the "Blue" in my code for whatever you want 4) This isn't a "do it for me" kind of site. $\endgroup$ Commented Mar 18, 2014 at 23:59

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.